Be positive, but not in 2017

Lemma: If $x,y$ are real numbers, we have: $\left|x\right|+\left|y\right|\ge\left|x+y\right|$ . The equation holds iff $xy\ge0$ .

Applying this lemma, we have:

$\quad \left| x+1 \right| +\left| x+5 \right| +\left| x+14 \right| +\left| x+97 \right| +\left| x+1920 \right|$

$=\left| -x-1 \right| +\left| x+1920 \right|+\left| -x-5 \right| +\left| x+97 \right|+\left| x+14 \right|$

$\ge\left|-x-1+x+1920\right|+\left|-x-5+x+97\right|+0$

$=2011$

The equality holds iff $x=-14$ .